1. You have 3500 in savings for 9 months at a rate of 4.5%. How much will you have at the end of that time?
Ans. my book says: 3,618.13
I come up with: 118,125
2. Scale reads 1 inch = 24 inches for a house window. If window measures 1 3/4 inches, what is the actual length?
Ans. my book says: 3 ft 6 in
I come with 3.5
3. Scale reads 1 inch = 8 ft. If the width of the drawing is 2.25 inches and the length is 4 inches, what is the actual length of the deck's diagonal?
Ans. my book says: 37 ft.
I don't know how they came up with 37 ft.
1.
amount = 3500 + 3500(.045)(9/12)
= 3500 + 118.125
= 3618.13
Your answer is only the interest earned, you must add this to what you already have.
2.
you have 3.5 feet
= 3 feet + 1/2 foot ----- .5 = 1/2
= 3feet , 6 inches
3.
so the actual width of the deck is 18 ft and the length is 32 feet
by Pythagoras
H^2 = 18^2 + 32^2 = 1348
H = √1348 = 36.7 or rounded to 37 feet
1.
Can't imagine how you got that answer. Even using 45%, I only get 99169!
However, 4.5% = .045 and that's an annual rate.
You want a monthly rate. Furthermore, you don't say whether that's simple interest or compounded monthly
Simple: 3500(1+.045/12*9) = 3618.13
so, I guess that's it.
2.
the scale indicates that the real dimensions are 24 times as large as the scale drawing.
1 3/4 = 7/4
7/4*24 = 42 inches = 3'6"
You are correct. Since a foot is 12 inches, the .5 foot is 6 inches.
3.5 feet = 3 feet 6 inches!
Keep track of the units, and don't lose track of conversions needed.
3.
This is just like #2.
1" = 8'
2.2" = 2.25(8') = 18'
4" = 4(8') = 32'
so, you have a rectangle that is 18x32.
Recall the Pythagorean Theorem, to see that the diagonal is
√(18^2+32^2) = √(324+1024) = √1348 = 36.7, or 37'
1. To calculate the amount you will have at the end of 9 months with a savings of $3500 at a rate of 4.5%, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future amount (what you'll have at the end)
P = the principal amount (initial savings)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, you have:
P = $3500
r = 4.5% (0.045 as a decimal)
n = 1 (compounded annually)
t = 9/12 = 0.75 (since 9 months is 9/12 of a year)
Plugging these values in, the calculation would be:
A = 3500(1 + 0.045/1)^(1*0.75)
A = 3500(1.045)^(0.75)
A ≈ $3636.28
Therefore, you should have approximately $3636.28 at the end of 9 months, not $118,125.
2. To find the actual length of a measurement based on a scale, you need to multiply the measurement on the scale by the scale factor.
In this case, the scale reads 1 inch = 24 inches. So, if the window measures 1 3/4 inches, you can convert that to inches by multiplying it by the scale factor:
Actual length = 1 3/4 inches * 24 inches
Actual length = (7/4) inches * 24 inches
Actual length = 7 * 6 inches
Actual length = 42 inches
So, the actual length of the window is 42 inches, not 3.5.
3. To determine the actual length of the deck's diagonal based on a scale, you need to use the scale factor.
The scale reads 1 inch = 8 feet. So, if the width of the drawing is 2.25 inches and the length is 4 inches, you can calculate the actual width and length of the deck:
Actual width = 2.25 inches * 8 feet/inch
Actual width = 18 feet
Actual length = 4 inches * 8 feet/inch
Actual length = 32 feet
Then, you can use the Pythagorean theorem to calculate the length of the diagonal:
d^2 = width^2 + length^2
d^2 = 18^2 + 32^2
d^2 = 324 + 1024
d^2 = 1348
d ≈ √1348
d ≈ 36.71 feet
So, the actual length of the deck's diagonal would be approximately 36.71 feet, not 37 feet.